Stochastic Optimization Methods

This chapter introduces some methods aimed at solving difficult optimization problems arising in many engineering fields. By difficult optimization problems, we mean those that are not convex. Recall that for the class of non-convex problems, there is no algorithm capable of guaranteeing, in reasonable a reasonable amount of time (By reasonable time, we mean polynomial in the size of the problem.), that the solution found is the global optimum. Under these conditions, we must be content with finding an acceptable solution. After introducing the notion of acceptable solution, a brief overview of the main stochastic methods which can be used for solving continuous non-convex constrained optimization problems is presented, i.e., Pure Random Search Methods (PRSM), Simulated Annealing (SA), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO). These methods are designed to produce an acceptable solution. The last part is dedicated to the problem of robust optimization, i.e., optimization in the presence of uncertainties on the problem data.